Controlled Authentication Semi-Quantum Key Agreement Protocol for the Internet of Medical Things

Yefeng He; Liaoyuan Shen; Yichi Zhang

doi:10.2478/qic-2026-0007

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Controlled Authentication Semi-Quantum Key Agreement Protocol for the Internet of Medical Things

Quantum Information & Computation

Volume 26 (2026): Issue 1 (March 2026)

By: Yefeng He, Liaoyuan Shen and Yichi Zhang

Open Access

|Jun 2026

Figures & Tables

Quantum circuit diagram for preparing and measuring a 4-Particle W States.

(a) Quantum circuit for case 1 in Table 2. (b) Quantum circuit for case 2 in Table 2 (similar to case 3 and case 5 in Table 2). (c) Quantum circuit for case 4 in Table 2 (similar to case 6 and case 7 in Table 2). (d) Quantum circuit for case 8 in Table 2.

(a) Run results of (a) in Figure 4. (b) Run results of (b) in Figure 4. (c) Run results of (c) in Figure 4. (d) Run results of (d) in Figure 4.

Measurement results of the quantum circuit in Figure 4 under noisy environment.

Quantum bit error rate under various noise levels.

Key generation rate under various noise levels.

Simulation-Experiment Parameter_

Platform	IBM Quantum
Software Development Kit	Qiskit(2.1.1)
Noise parameters (amplitude damping noise, depolarizing noise)	(0.001,0.01)(0.005,0.02)(0.01,0.03)(0.02,0.04)

Comparison of the proposed CASQKA protocol with other protocols_

Protocol	Quantum resource	Identity authentication function	Semi-quantum properties	Qubit efficiency (%)
Ref. [36]	Cluster states	No	Yes	2.08
Ref. [28]	Cluster states	No	Yes	1.60
Ref. [39]	Five qubit entangled states	Yes	No	7.70
Ref. [40]	Bell states	No	Yes	6.70
Ref. [25]	Bell states	Yes	No	16.67
Ref. [22]	Four-particle GHZ states	Yes	No	53.33
Ref. [49]	Single-particle states	Yes	No	16.67
Ref. [50]	three-particle GHZ-like states	No	Yes	16.67
Proposed protocol	W states	Yes	Yes	2.43

Communication complexity comparison_

Metric	Proposed protocol	Ref [5]
Quantum communication complexity	30n qubits	n qubits
Classical communication complexity	3n classical bits	~0.5n classical bits
Total communication complexity	33n bits	1.5n bits
Qubit efficiency (η)	3.03%	~66.67%

All operational scenarios of Bob, Charlie, and Dave_

Case	Bob	Charlie	Dave	Protocol phase
1	CTRL	CTRL	CTRL
2	CTRL	CTRL	SIFT
3	CTRL	SIFT	CTRL
4	CTRL	SIFT	SIFT	Security check
5	SIFT	CTRL	CTRL
6	SIFT	CTRL	SIFT
7	SIFT	SIFT	CTRL
8	SIFT	SIFT	SIFT	Key agreement

Variable-Meaning_

I_B, I_C, I_D	Bob/Charlie/Dave’s pre-shared identity bit strings (n bits)
K_A, K_B, K_C, K_D	Each party’s private key string (n bits)
S_A, S_B, S_C, S_D	The four-particle sequences of the W state are held by Alice, Bob, Charlie, and Dave, respectively.
V_B, V_C, V_D	The n-bit outcomes of Z-basis measurements performed by Bob/Charlie/Dave at the SIFT positions.
VBVC,VDV_B^V_C^,V_D^	The XOR of the measurement outcome with the identity string, VB={ VB(1)⊕IB(1),VB(2)⊕IB(2),VB(3)⊕IB(3)…VB(n)⊕IB(n) }V_B^ = \left\{ {V_B^{(1)} \oplus I_B^{(1)},V_B^{(2)} \oplus I_B^{(2)},V_B^{(3)} \oplus I_B^{(3)} \ldots V_B^{(n)} \oplus I_B^{(n)}} \right\} used for authentication.
V_AB, _AC, V_AD	The classical bit string actually measured by Alice at the corresponding positions, used for comparison and verification.
RB,RC,RDRB′,RC′,RD′K{{R_B},{R_C},{R_D}}	The n-bit SIFT measurement results of Bob/Charlie/Dave in Case-8 used to conceal the private key the final 4-party shared key
K_AB, K_AC, K_AD	The key segments permuted by Alice using I_B, I_C, I_D are sent to Bob/Charlie/Dave, respectively.

Encoding rules_

Quantum states	Classical bits
\|0〉	0
\|1〉	1

References

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Articles in this issue

DOI: https://doi.org/10.2478/qic-2026-0007 | Journal eISSN: 3106-0544 | Journal ISSN: 1533-7146

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Language: English

Page range: 129 - 153

Submitted on: Oct 12, 2025

Accepted on: Jan 6, 2026

Published on: Jun 4, 2026

Published by: Cerebration Science Publishing Co., Limited

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

quantum key agreement,

W states,

semi-quantum key agreement,

identity authentication

Related subjects:

Physics,

Computer sciences in the humanities,

Computer sciences,

Computer sciences in natural sciences

© 2026 Yefeng He, Liaoyuan Shen, Yichi Zhang, published by Cerebration Science Publishing Co., Limited
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 26 (2026): Issue 1 (March 2026)

Controlled Authentication Semi-Quantum Key Agreement Protocol for the Internet of Medical Things

Figures & Tables

Figure 1.

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Simulation-Experiment Parameter_

Comparison of the proposed CASQKA protocol with other protocols_

Communication complexity comparison_

All operational scenarios of Bob, Charlie, and Dave_

Variable-Meaning_

Encoding rules_

Paradigm

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